Solve the Linear Programming Problem $\mathrm { P } _ { 1 }$

question 193

Multiple Choice

Solve the linear programming problem.
-An airline with two types of airplanes, $\mathrm { P } _ { 1 }$ and $\mathrm { P } _ { 2 }$ , has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers. For a certain trip, airplane $P _ { 1 }$ costs $\$ 10,000$ to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane $P _ { 2 }$ costs $\$ 8500$ to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

• A) \(11 \mathrm { P } _ { 1 }\) planes and \(7 \mathrm { P } _ { 2 }\) planes
• B) \(7 \mathrm { P } _ { 1 }\) planes and \(11 \mathrm { P } _ { 2 }\) planes
• C) \(5 \mathrm { P } _ { 1 }\) planes and \(17 \mathrm { P } _ { 2 }\) planes
• D) \(9 \mathrm { P } _ { 1 }\) planes and \(13 \mathrm { P } _ { 2 }\) planes

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Definitions:

Profit-Maximizing Firm

A business entity whose primary goal is to achieve the highest possible profit from its operations.

Marginal Cost

The cost added by producing one more unit of a product or service, a key concept in economics determining optimal production levels.

Concentration Ratio

A measurement of the market share held by the largest firms within an industry, indicating the degree of market control.

Monopolistic Competitor

A business operating in a market structure characterized by many firms selling products that are similar but not identical, allowing for significant differentiation and competition.